My sister i don't think she hates you other wise you wouldn't be in the same house, she doesn't mean it she is just properly stressed and maybe you and your siblings are not helping her .
you have to ask your self what are you doing that is causing this, is your mother struggling with the children,the house work,bills .
Communication is the key . Sit down with her maybe do something nice buy her a gift, put a plan down to the house work few times a week . Help her with your siblings . she will come around she loves you be a friend talk to her. Don't lose your family they are the most important thing in your life. Appreciate what you have and try to focus on your mother/family goodness , recalling kindness they have done for you and overlooking their faults you're relationships will last the test of time and manifest comfort.